Explain the formation of a waterfall

As water flows over underlying rocks, it erodes softer rock much faster than harder rock. This creates a small step in the stream or river.

Explaining the formation of waterfalls

As water flows over underlying rocks, it erodes softer rock much faster than harder rock. This creates a small step in the stream or river.
Over time this step gets larger and the harder rock is undercut.
This eventually creates an overhang of the hard rock, which collapses with a lack of support. These rocks fall into the plunge pool at the bottom of the step/waterfall and aid erosion as they are swirled around. 
The waterfall moves upstream as this process is repeated and a steep-sided gully is eventually formed.